{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:44:47Z","timestamp":1774953887773,"version":"3.50.1"},"reference-count":36,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2015,1,9]],"date-time":"2015-01-09T00:00:00Z","timestamp":1420761600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. symb. logic"],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, \u2018a proposition is noncontingent\u2019 means that you know<jats:italic>whether<\/jats:italic>the proposition is true. In this paper, we study contingency logic with the noncontingency operator \u0394 but without the necessity operator \u25a1. This logic is not a normal modal logic, because \u0394(<jats:italic>\u03c6<\/jats:italic>\u2192<jats:italic>\u03c8<\/jats:italic>) \u2192 (\u0394<jats:italic>\u03c6<\/jats:italic>\u2192 \u0394<jats:italic>\u03c8<\/jats:italic>) is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over<jats:italic>symmetric<\/jats:italic>frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the \u2018almost-definability\u2019 schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other\u2019s work. One goal of our paper is to bridge this gap.<\/jats:p>","DOI":"10.1017\/s1755020314000343","type":"journal-article","created":{"date-parts":[[2015,1,9]],"date-time":"2015-01-09T09:23:52Z","timestamp":1420795432000},"page":"75-107","source":"Crossref","is-referenced-by-count":61,"title":["CONTINGENCY AND KNOWING WHETHER"],"prefix":"10.1017","volume":"8","author":[{"given":"JIE","family":"FAN","sequence":"first","affiliation":[]},{"given":"YANJING","family":"WANG","sequence":"additional","affiliation":[]},{"given":"HANS VAN","family":"DITMARSCH","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,1,9]]},"reference":[{"key":"S1755020314000343_ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-012-0233-5"},{"key":"S1755020314000343_ref36","first-page":"434","volume-title":"Proceedings of the 13th International Congress of Linguists","author":"Zuber","year":"1982"},{"key":"S1755020314000343_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01661170"},{"key":"S1755020314000343_ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5839-4"},{"key":"S1755020314000343_ref2","first-page":"21","volume-title":"Proceedings of 21st ECAI","author":"Attamah","year":"2014"},{"key":"S1755020314000343_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(05)82606-4"},{"key":"S1755020314000343_ref24","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2008-018"},{"key":"S1755020314000343_ref25","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1145\/860575.860839","volume-title":"Proceedings of 2nd AAMAS","author":"van der Hoek","year":"2003"},{"key":"S1755020314000343_ref34","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1305\/ndjfl\/1012429717","article-title":"Completeness and definability in the logic of noncontingency","volume":"40","author":"Zolin","year":"1999","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1755020314000343_ref8","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1163\/18756735-90000845","article-title":"Question-embedding and factivity","volume":"77","author":"\u00c9gr\u00e9","year":"2008","journal-title":"Grazer Philosophische Studien"},{"key":"S1755020314000343_ref23","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4074.001.0001","volume-title":"Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems","author":"Reiter","year":"2001"},{"key":"S1755020314000343_ref19","first-page":"318","article-title":"Contingency and non-contingency bases for normal modal logics","volume":"9","author":"Montgomery","year":"1966","journal-title":"Logique et Analyse"},{"key":"S1755020314000343_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-009-9646-1"},{"key":"S1755020314000343_ref32","first-page":"569","article-title":"Conditionally knowing what","volume":"10","author":"Wang","year":"2014","journal-title":"Advances in Modal Logic"},{"key":"S1755020314000343_ref15","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1305\/ndjfl\/1040248455","article-title":"The logic of noncontingency","volume":"36","author":"Humberstone","year":"1995","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1755020314000343_ref10","unstructured":"Hansen J . 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